The Euler–Lagrange equation is a fundamental equation in the calculus of variations, which is a field of mathematics that deals with optimizing functionals. A functional is typically an integral that depends on a function and its derivatives. In particular, the Euler–Lagrange equation is used to find the function (or functions) that will minimize (or maximize) a certain integral, usually representing some physical quantity, such as action in physics.
The Minkowski–Steiner formula is a result in convex geometry that describes the relationship between the volumes of Minkowski sums of sets. In particular, it provides a way to calculate the volume of the Minkowski sum of a convex body and a scaled version of another convex set.
The Palais–Smale compactness condition is a criterion used in the context of variational methods and critical point theory, particularly when dealing with the analysis of functionals on Banach spaces or Hilbert spaces. It plays a crucial role in the study of minimization problems and the existence of critical points.
Henri Hogbe Nlend was a prominent Cameroonian politician and historian who played a significant role in Cameroon's post-independence politics. He is known for his contributions to the understanding of Cameroon's history and politics, particularly regarding the country's transition from colonial rule to independence. He was involved in the political scene during the period of decolonization in Africa and engaged with various political movements and parties within Cameroon.
Jim Bohlen is best known as an environmental activist and one of the co-founders of the organization Greenpeace. He played a significant role in raising awareness about environmental issues, particularly relating to nuclear testing and the protection of the environment. Bohlen was part of the group that organized the first Greenpeace mission in 1971 to prevent nuclear testing in Alaska. His activism contributed to the growth of the global environmental movement.
Multipolar exchange interaction refers to the interaction between localized magnetic moments (such as those from electron spins) that arises from higher-order multipole expansions of their magnetic fields. While traditional exchange interactions (like the Heisenberg exchange) typically involve simple dipole interactions between neighboring spins, multipolar interactions can include contributions from quadrupole and octupole moments, and beyond.
Gottfried Keller, a prominent Swiss poet and novelist of the 19th century, is known for his rich and evocative poetry. His works have inspired various musical settings, particularly in the realm of art song (Lied). Composers have been drawn to Keller's lyrical style and thematic depth, which often explore nature, love, and the human condition.
"Music Music Music" can refer to a few different things depending on the context: 1. **Song**: "Music Music Music" is a popular song written by Stephen Weiss and recorded by various artists, including the legendary American singer Teresa Brewer in the 1950s. The song celebrates the joy and excitement of music itself. 2. **Event/Concept**: It can refer to an event, festival, or concept centered around music, emphasizing the importance of music in culture and society.
"Mystery of the Wax Museum" is a 1933 horror film directed by Michael Curtiz. It's notable for being one of the earliest films made using the two-color Technicolor process. The story revolves around a series of murders connected to a wax museum that features lifelike wax figures. A newspaper reporter investigates the sinister activities occurring in the museum, uncovering dark secrets and confronting the sinister mastermind behind the wax figures.
The N400 is a component of the event-related potential (ERP) that is observed in electroencephalography (EEG) studies. It is typically associated with language processing and is characterized by a negative voltage peak that occurs approximately 400 milliseconds after the presentation of a stimulus, particularly in response to semantic violations or unexpected words in a sentence. For example, if a sentence ends with a word that does not fit semantically with the preceding context (e.g.
Nameplate capacity, also known as rated capacity, is the maximum output that a power plant or generator can produce under specific conditions, typically measured in megawatts (MW) for power plants. This capacity is determined by the manufacturer and indicates the ideal performance level of the equipment. Key points about nameplate capacity include: 1. **Standard Conditions**: The nameplate capacity is usually based on standard operating conditions, which may include factors like temperature, humidity, and fuel quality.
Nancy E. Heckman is a notable statistician and professor known for her work in the fields of statistics and biostatistics, particularly in developing statistical methods for health and social sciences research. She has made significant contributions in areas such as missing data, causal inference, and statistical methodology. Heckman is also known for the Heckman selection model, which addresses sample selection bias—an important consideration in econometrics and various fields that rely on observational data.
Nanoarchitectonics is a field of research that focuses on the design and construction of functional materials and systems at the nanoscale level. It involves the manipulation and organization of nanoscale components, such as molecules, nanostructures, and nanoparticles, to create new materials and devices with specific properties or functions.
A nanonetwork is a network of interconnected nanoscale devices, typically operating at the nanoscale level (on the order of 1 to 100 nanometers). These devices often include nanosensors, nanoactuators, and other nanotechnologies that can communicate with each other and work collaboratively to perform specific tasks or gather information.
A nanosubmarine is a type of very small submarine, often at the nanoscale level, designed for various specialized applications, typically in the field of nanotechnology and biomedical research. These tiny submarines are sometimes envisioned or developed for purposes such as targeted drug delivery in the human body, environmental monitoring, or as platforms for conducting scientific experiments at the molecular level.
Nanotechnology publications refer to academic articles, research papers, reviews, and conference proceedings that focus on the field of nanotechnology. This interdisciplinary area of study involves the manipulation and understanding of materials and systems at the nanoscale, typically between 1 and 100 nanometers.
The π-calculus (pi-calculus) is a process calculus introduced by Robin Milner in the 1990s as a formal model for describing and analyzing concurrent systems and mobile processes. It extends earlier formalisms, such as the CCS (Calculus of Communicating Systems), and is designed to model how processes interact with each other through communication, especially in scenarios where the structure and behavior of these processes can change over time (e.g., due to mobility).
The National Defense Industrial Association (NDIA) is a nonprofit organization in the United States that serves as a forum for government and industry to engage in discussions related to national security and defense. Founded in 1919, the NDIA aims to promote the understanding of defense issues, support the defense industrial base, and foster collaboration between defense contractors, military leaders, and government officials.
In the National Football League (NFL), uniform numbers are used to identify players on the field, and they are assigned according to specific guidelines set by the league. Here are some key points regarding NFL uniform numbers: 1. **Numbering Categories**: Players are assigned numbers based on their positions, which are grouped into different categories. For example: - Quarterbacks, kickers, and punters typically wear numbers 1-19.
The National Institute of Statistics and Census of Argentina (Instituto Nacional de Estadística y Censos, or INDEC) is the official government body responsible for collecting, analyzing, and disseminating statistical information in Argentina. Established in 1968, INDEC's primary role is to provide reliable and accurate data concerning various sectors of the economy and society, including demographics, economic indicators, employment statistics, and social conditions.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact